让语言模型直接用代码思考，提升数学推理准确率
Teaching Language Models to Think in Code
- 用代码作为核心推理工具，取代自然语言与代码交替的旧模式
- 在5个数学竞赛题上超越所有基线，40亿参数模型胜过2350亿参数大模型
- 99.2%的答案基于代码执行结果，能自动修复执行错误，适合追求高精度推理的研究者
工具集成推理（TIR）是当前语言模型解决数学问题的主要范式，结合自然语言推理与代码执行。但该方法存在三大局限：代码常作为事后验证，中间自然语言计算易出错，且自然语言与代码角色重叠。本文提出ThinC（Thinking in Code）框架，使代码本身成为推理主体而非辅助工具。ThinC先进行简短的自然语言规划，随后所有推理通过仅由执行输出连接的代码块完成。我们从教师模型中蒸馏出12.2k条以代码为中心的推理轨迹，并对ThinC-1.7B和ThinC-4B进行监督微调与强化学习训练。ThinC-4B在五个竞赛级数学基准上持续优于所有TIR基线，甚至超过更大的Qwen3-235B-A22B-Thinking模型。分析显示，99.2%的最终答案基于解释器输出，且模型可在不依赖自然语言干预的情况下可靠恢复代码执行失败。
原文摘要 · Abstract (English)
Tool-integrated reasoning (TIR) has emerged as a dominant paradigm for mathematical problem solving in language models, combining natural language (NL) reasoning with code execution. However, this interleaved setup has three key limitations: code often acts as a post-hoc verifier, intermediate NL computations are error-prone, and NL and code play overlapping rather than clearly distinct roles. We propose ThinC (Thinking in Code), a framework in which code itself serves as the reasoner rather than as a tool invoked by NL. A ThinC trajectory begins with a brief NL planning step, after which all reasoning unfolds through code blocks connected only by their execution outputs. We distill 12.2k code-centric trajectories from a teacher model and train ThinC-1.7B and ThinC-4B with supervised fine-tuning followed by reinforcement learning. ThinC-4B consistently outperforms every TIR baseline on five competition-level math benchmarks and even surpasses the much larger Qwen3-235B-A22B-Thinking. Further analysis shows that ThinC reasons through code: 99.2% of its final answers are grounded in interpreter output, and the model recovers reliably from code execution failures without intermediate NL reasoning. Our code and models will be released soon.
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